Chromatic aberration distortions such as wavelength-dependent blur are caused by imperfections in photographic lenses. These distortions are much more severe in the case of color and near-infrared joint acquisition, as a wider band of wavelengths is captured. In this paper, we consider a scenario where the color image is in focus, and the NIR image captured with the same lens and same focus settings is out-of-focus and blurred. To reduce chromatic aberration distortions, we propose an algorithm that estimates the blur kernel and deblurs the NIR image using the sharp color image as a guide in both steps. In the deblurring step, we retrieve the lost details of the NIR image by exploiting the sharp edges of the color image, as the gradients of color and NIR images are often correlated. However, differences of scene reflections and light in visible and NIR bands cause the gradients of color and NIR images to be different in some regions of the image. To handle this issue, our algorithm measures the similarities and differences between the gradients of the NIR and color channels. The similarity measures guide the deblurring algorithm to efficiently exploit the gradients of the color image in reconstructing
high-frequency details of NIR, without discarding the inherent differences between these images. Simulation results verify the effectiveness of our algorithm, both in estimating the blur kernel and deblurring the NIR image, without producing ringing artifacts inherent to the results of most deblurring methods.
KEYWORDS: Mathematical modeling, Matrices, Wavelets, Monte Carlo methods, Differential equations, Applied sciences, Algorithm development, Source localization, Social sciences, Current controlled current source
Epidemic models on networks have long been studied by biologists and social sciences to determine the steady state levels of an infection on a network. Recently, however, several authors have begun considering the more difficult problem of estimating the source of an infection given information about its behavior some time after the initial infection. In this paper, we describe a technique to estimate the source of an infection on a general graph based on observations from a small set of observers during a fixed time window at some unknown time after the initial infection. We describe an alternate representation for the susceptible-infected (SI) infection model based on geodesic distances on a randomly-weighted version of the graph; this representation allows us to exploit fast algorithms to compute geodesic distances to estimate the marginal distributions for each observer and compute a pseudo-likelihood function that is maximized to find the source.
We present a novel image sensor for high dynamic range imaging. The sensor performs an adaptive one-bit quantization at each pixel, with the pixel output switched from 0 to 1 only if the number of photons reaching that pixel is greater than or equal to a quantization threshold. With an oracle knowledge of the incident light
intensity, one can pick an optimal threshold (for that light intensity) and the corresponding Fisher information
contained in the output sequence follows closely that of an ideal unquantized sensor over a wide range of intensity
values. This observation suggests the potential gains one may achieve by adaptively updating the quantization thresholds. As the main contribution of this work, we propose a time-sequential threshold-updating rule that asymptotically approaches the performance of the oracle scheme. With every threshold mapped to a number of
ordered states, the dynamics of the proposed scheme can be modeled as a parametric Markov chain. We show that the frequencies of different thresholds converge to a steady-state distribution that is concentrated around the optimal choice. Moreover, numerical experiments show that the theoretical performance measures (Fisher
information and Cram´er-Rao bounds) can be achieved by a maximum likelihood estimator, which is guaranteed to find globally optimal solution due to the concavity of the log-likelihood functions. Compared with conventional image sensors and the strategy that utilizes a constant single-photon threshold considered in previous work, the proposed scheme attains orders of magnitude improvement in terms of sensor dynamic ranges.
A cost-effective and convenient approach for color imaging is to use a single sensor and mount a color filter
array (CFA) in front of it, such that at each spatial position the scene information in only one color channel is
captured. To estimate the missing colors at each pixel, a demosaicing algorithm is applied to the CFA samples.
Besides the filter arrangement and the demosaicing method, the spectral sensitivity functions of the CFA filters
considerably affect the quality of the demosaiced image. In this paper, we propose an algorithm to compute the
optimum spectral sensitivities of filters in the single sensor imager. The proposed algorithm solves a constrained
optimization problem to find optimum spectral sensitivities and the corresponding linear demosaicing method.
An important constraint for this problem is the smoothness of spectral sensitivities, which is imposed by modeling
these functions as a linear combination of several smooth kernels. Simulation results verify the effectiveness of
the proposed algorithm in finding optimal spectral sensitivity functions, which outperform measured camera
The classical uncertainty principle provides a fundamental tradeoff in the localization of a function in the time
and frequency domains. In this paper we extend this classical result to functions defined on graphs. We justify
the use of the graph Laplacian's eigenbasis as a surrogate for the Fourier basis for graphs, and define the notions
of "spread" in the graph and spectral domains. We then establish an analogous uncertainty principle relating
the two quantities, showing the degree to which a function can be simultaneously localized in the graph and
We have studied a camera with a very large number of binary pixels referred to as the gigavision camera  or the
gigapixel digital film camera [2, 3]. Potential advantages of this new camera design include improved dynamic
range, thanks to its logarithmic sensor response curve, and reduced exposure time in low light conditions, due
to its highly sensitive photon detection mechanism.
We use maximum likelihood estimator (MLE) to reconstruct a high quality conventional image from the binary
sensor measurements of the gigavision camera. We prove that when the threshold T is "1", the negative loglikelihood
function is a convex function. Therefore, optimal solution can be achieved using convex optimization.
Base on filter bank techniques, fast algorithms are given for computing the gradient and the multiplication of
a vector and Hessian matrix of the negative log-likelihood function. We show that with a minor change, our
algorithm also works for estimating conventional images from multiple binary images.
Numerical experiments with synthetic 1-D signals and images verify the effectiveness and quality of the
proposed algorithm. Experimental results also show that estimation performance can be improved by increasing
the oversampling factor or the number of binary images.
Color image demosaicking is a key process in the digital imaging pipeline. In this paper, we present a rigorous
treatment of a classical demosaicking algorithm based on alternating projections (AP). Since its publication, the
AP algorithm has been wildly cited and served as a benchmark in a flurry of papers in the demosaicking literature.
Despite its impressive performances, a relative weakness of the AP algorithm is its high computational complexity.
In our work, we provide a rigorous analysis of the convergence of the AP algorithm based on the concept of
contraction mapping. Furthermore, we propose an efficient noniterative implementation of the AP algorithm in
the polyphase domain. Numerical experiments show that the proposed noniterative implementation achieves the
same results obtained by the original AP algorithm at convergence, but is about an order of magnitude faster
than the latter.
Most digital cameras employ a spatial subsampling process, implemented as a color filter array (CFA), to capture
color images. The choice of CFA patterns has a great impact on the performance of subsequent reconstruction
(demosaicking) algorithms. In this work, we propose a quantitative theory for optimal CFA design. We view
the CFA sampling process as an encoding (low-dimensional approximation) operation and, correspondingly,
demosaicking as the best decoding (reconstruction) operation. Finding the optimal CFA is thus equivalent to
finding the optimal approximation scheme for the original signals with minimum information loss. We present
several quantitative conditions for optimal CFA design, and propose an efficient computational procedure to
search for the best CFAs that satisfy these conditions. Numerical experiments show that the optimal CFA
patterns designed from the proposed procedure can effectively retain the information of the original full-color
images. In particular, with the designed CFA patterns, high quality demosaicking can be achieved by using
simple and efficient linear filtering operations in the polyphase domain. The visual qualities of the reconstructed
images are competitive to those obtained by the state-of-the-art adaptive demosaicking algorithms based on the
We study a sampling problem where sampled signals come from a known union of shift-invariant subspaces
and the sampling operator is a linear projection of the sampled signals into a fixed shift-invariant subspace.
In practice, the sampling operator can be easily implemented by a multichannel uniform sampling procedure.
We present necessary and sufficient conditions for invertible and stable sampling operators in this framework,
and provide the corresponding minimum sampling rate. As an application of the proposed general sampling
framework, we study the specific problem of spectrum-blind sampling of multiband signals. We extend the previous results of Bresler et al. by showing that a large class of sampling kernels can be used in this sampling problem, all of which lead to stable sampling at the minimum sampling rate.
A system for automatic detection of pelvic lymph nodes is developed by incorporating complementary information
extracted from multiple MR sequences. A single MR sequence lacks sufficient diagnostic information for lymph
node localization and staging. Correct diagnosis often requires input from multiple complementary sequences
which makes manual detection of lymph nodes very labor intensive. Small lymph nodes are often missed even by
highly-trained radiologists. The proposed system is aimed at assisting radiologists in finding lymph nodes faster
and more accurately. To the best of our knowledge, this is the first such system reported in the literature. A
3-dimensional (3D) MR angiography (MRA) image is employed for extracting blood vessels that serve as a guide
in searching for pelvic lymph nodes. Segmentation, shape and location analysis of potential lymph nodes are then
performed using a high resolution 3D T1-weighted VIBE (T1-vibe) MR sequence acquired by Siemens 3T scanner.
An optional contrast-agent enhanced MR image, such as post ferumoxtran-10 T2*-weighted MEDIC sequence, can also be incorporated to further improve detection accuracy of malignant nodes. The system outputs a list of potential lymph node locations that are overlaid onto the corresponding MR sequences and presents them
to users with associated confidence levels as well as their sizes and lengths in each axis. Preliminary studies
demonstrates the feasibility of automatic lymph node detection and scenarios in which this system may be used
to assist radiologists in diagnosis and reporting.
With the ever increasing computational power of modern day processors, it has become feasible to use more
robust and computationally complex algorithms that increase the resolution of images without distorting edges
and contours. We present a novel image interpolation algorithm that uses the new contourlet transform to
improve the regularity of object boundaries in the generated images. By using a simple wavelet-based linear
interpolation scheme as our initial estimate, we use an iterative projection process based on two constraints
to drive our solution towards an improved high-resolution image. Our experimental results show that our new
algorithm significantly outperforms linear interpolation in subjective quality, and in most cases, in terms of
PSNR as well.
In 1992, Bamberger and Smith proposed the directional filter bank (DFB) for an efficient directional decomposition of two-dimensional (2-D) signals. Due to the nonseparable nature of the system, extending the DFB to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem. This paper proposes a new family of filter banks, named 3DDFB, that can achieve the directional decomposition of 3-D signals with a simple and efficient tree-structured construction. The ideal passbands of the proposed 3DDFB are rectangular-based pyramids radiating out from the origin at different orientations and tiling the whole frequency space. The proposed 3DDFB achieves perfect reconstruction. Moreover, the angular resolution of the proposed 3DDFB can be iteratively refined by invoking more levels of decomposition through a simple expansion rule. We also introduce a 3-D directional multiresolution decomposition, named the surfacelet transform, by combining the proposed 3DDFB with the Laplacian pyramid. The 3DDFB has a redundancy factor of 3 and the surfacelet transform has a redundancy factor up to 24/7.
Directional multiresolution image representations have lately attracted much attention. A number of new systems, such as the curvelet transform and the more recent contourlet transform, have been proposed. A common issue of these transforms is the redundancy in representation, an undesirable feature for certain applications (e.g. compression). Though some critically sampled transforms have also been proposed in the past, they can only provide limited directionality or limited flexibility in the frequency decomposition. In this paper, we propose a filter bank structure achieving a nonredundant multiresolution and multidirectional expansion of images. It can be seen as a critically sampled version of the original contourlet transform (hence the name CRISP-contourets) in the sense that the corresponding frequency decomposition is similar to that of contourlets, which divides the whole spectrum both angularly and radially. However, instead of performing the multiscale and directional decomposition steps separately as is done in contourlets, the key idea here is to use a combined iterated nonseparable filter bank for both steps. Aside from critical sampling, the proposed transform possesses other useful properties including perfect reconstruction, flexible configuration of the number of directions at each scale, and an efficient tree-structured implementation.